CN113919147A - Oil reservoir fracturing fracture network expansion path calculation method - Google Patents

Oil reservoir fracturing fracture network expansion path calculation method Download PDF

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CN113919147A
CN113919147A CN202111148918.7A CN202111148918A CN113919147A CN 113919147 A CN113919147 A CN 113919147A CN 202111148918 A CN202111148918 A CN 202111148918A CN 113919147 A CN113919147 A CN 113919147A
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赵辉
盛广龙
周玉辉
饶翔
钟珣
刘伟
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Yangtze University
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Abstract

The invention discloses a method for calculating a fracture propagation path, which comprises the steps of acquiring geological parameters of various reservoirs required to be used in the fracture propagation process, and determining the circumferential stress distribution formed by the tip of a fracture and the critical fracture stress of each geological unit body around the tip of the fracture according to the geological parameters of the various reservoirs and the distribution rule of natural fractures; for a geological unit body with a formed secondary fracture, when the circumferential stress around the fracture tip is greater than the critical fracture stress, the fracture morphology is output. The method also calculates the crack initiation stress intensity according to the circumferential stress and the crack initiation critical stress; determining the crack propagation probability of each geological unit body around the secondary crack tip according to the crack initiation stress intensity and the fractal probability index; and determining the crack propagation direction by combining all the crack propagation probabilities. According to the method, the problem that the description of a deterministic fracture propagation simulation method is unclear due to unclear reservoir parameters is solved through the fractal probability index.

Description

Oil reservoir fracturing fracture network expansion path calculation method
Technical Field
The invention relates to the field of fracture propagation paths, in particular to a method for calculating a network propagation path of a fracture of an oil reservoir.
Background
The reservoir fracturing can generate hydraulic fractures with high flow conductivity and form a complex secondary fracture network system, which provides support for the development of unconventional oil and gas economic benefits.
Describing the network form of the fracturing fracture is a basic premise for evaluating the fracturing effect and dynamically simulating production, and as various physical phenomena in the nature are similar to the formation mechanism and the expansion rule of the fracturing fracture of a reservoir stratum, taking a lightning formation process as an example. Because of the uneven space electric field distributed in the space and the lightning originated from the ultra-high potential generated by the positive and negative charged cloud layers, when the energy is larger than the critical breakdown field intensity of the space medium, the medium between two points is broken down to become an electric conductor, and a lightning extension path is formed. Meanwhile, the formed lightning channel changes the electric field distribution of the surrounding space, thereby influencing the forming and distribution rules of the subsequent lightning path. Similarly, the heterogeneity of the ground stress and the rock mechanical parameters of the unconventional reservoir is strong, the fracturing fluid flows into a pre-perforated channel from a wellhead device through a shaft in the oil reservoir fracturing process, the pressure is suppressed in the bottom of the well and the perforated channel, when the fracturing fluid pressure is greater than the rock fracturing pressure, the rock is damaged to form a communicated fracture channel, and the fracturing fluid transmits high-pressure energy through the fracture channel, so that a fracture expansion path is formed.
Although the conventional scheme can well perform the expansion calculation of the fracture network, the expansion problem of the fracture network is converted into a boundary integral equation by taking a boundary element method as an example, and the problem is solved by analyzing the boundary integral equation. The method is suitable for processing the complicated crack network problem, but the simulation of the fluid-solid coupling problem by using the method has great difficulty and is not beneficial to improving the simulation efficiency of crack network expansion.
Disclosure of Invention
The invention aims to solve the technical problem of improving the simulation efficiency of fracture network expansion and provides a method for calculating an expansion path of a fracture network of oil reservoir fracturing.
The technical scheme adopted by the invention for solving the technical problems is as follows: a calculation method for an expansion path of a reservoir fracturing fracture network is constructed, and comprises the following steps:
s1, dividing the stratum into a plurality of geological unit bodies with certain sizes;
s2, determining an initial fracture coordinate point;
s3, aiming at each geological unit body, when fracturing fluid permeates into cracks, introducing a fluid pressure drop equation to correct flow pressure in the cracks, and calculating the pressure of the fracturing fluid permeating fluid in the cracks of the corresponding geological unit body;
s4, acquiring all reservoir geological parameters needed in the process of fracturing fracture expansion, and determining the circumferential stress distribution formed by the fracture tip and the critical fracture stress of all geological unit bodies around according to the reservoir geological parameters and the natural fracture distribution rule; the geological parameters of the reservoir comprise a ground stress field, fracture initiation critical stress, flow pressure in the fracture and a stress shadow effect of the fracture;
s5, aiming at the geological unit body with the formed secondary fractures, when the circumferential stress around the fracture tips is larger than the critical fracture stress, the fracture morphology is output, and if not, the next step is executed;
s6, calculating the fracture initiation stress intensity according to the circumferential stress and the fracture initiation critical stress; introducing a fractal probability index, and determining the crack propagation probability of each geological unit body around the secondary crack tip according to the crack initiation stress intensity and the fractal probability index;
s7, determining the crack propagation direction by combining the crack propagation probabilities;
and S8, correcting the stress change influence on the corresponding geological unit bodies after the fracture network extends along the fracture extension direction by adopting the stress shadow effect, and returning to the step S4 until the fracture extension does not occur any more.
Further, in step S1, a total of 200 × 200 geological unit bodies are obtained by division, and the control range of each unit geological body is 1 × 2 m.
Further, in step S3, the fluid pressure drop equation is specifically:
Figure BDA0003286432110000031
wherein v isxRepresenting the fluid flow velocity up the fracture axis, μ the fluid viscosity, p the fluid pressure within the fracture, x the fracture axis direction, y the fracture width direction, and z the fracture height direction.
Further, in step S6, the calculating the fracture initiation stress strength according to the circumferential stress and the fracture initiation critical stress includes:
and (3) calculating the fracture initiation stress intensity according to the following formula:
Figure BDA0003286432110000032
wherein σfrStress intensity for crack initiation, σθIs the circumferential stress, σcrCritical stress for crack initiation; r is the distance from the initiation point to the tip of the fracture; theta is a stress angle; k1Is the first crack stress intensity factor, K2Is a second fracture stress intensity factor; kICFracture toughness at the tip of the fracture.
Further, a first crack stress intensity factor K1The comprehensive action of the ground stress and the fluid pressure in the seam is specifically represented as:
Figure BDA0003286432110000033
wherein alpha is an included angle between the normal direction of the crack surface and a coordinate axis; a represents the half-length of the crack; p is a radical ofnetIs the fracture net pressure.
Further, a second crack stress intensity factor K2The comprehensive action of the ground stress and the fluid pressure in the seam is specifically represented as:
Figure BDA0003286432110000034
wherein σxxAnd σyyExpressed as stress in the principal and normal directions of the fracture, respectively; alpha is an included angle between the normal direction of the crack surface and the coordinate axis; a represents the half length of the crack.
Further, in step S6, the determining the fracture propagation probability of each geological unit body around the secondary fracture tip according to the fracture initiation stress intensity and the fractal probability index includes:
the calculation of the fracture propagation probability is performed by the following formula:
Figure BDA0003286432110000041
wherein σθIs the circumferential stress, σcrIs fracture initiation critical stress, eta is fractal probability index, p (i, j) is fracture propagation probability, N is total breakdown point number, (sigma)θ-σcr)(i,j)The fracture initiation stress intensity at the point (i, j).
Further, in step S7, the determining the crack propagation direction by combining the crack propagation probabilities includes:
determining a stress difference gradient, wherein when the stress difference gradient is larger, the crack is expanded towards the direction of large stress difference;
determining the injection pressure of the fracturing fluid, wherein the larger the injection pressure of the fracturing fluid is, the larger the expansion distance of the fracture is;
determining a fractal probability index, wherein when the fractal probability index is larger, the crack is expanded towards a breakable point.
The method for calculating the network expansion path of the oil reservoir fracturing fracture has the following beneficial effects:
1. the fracture crack simulation method based on the breakdown path determines the crack extension direction, so that the crack extension simulation efficiency is greatly improved;
2. the uncertainty of the crack propagation direction is represented through the fractal probability index, so that the problem that the description of a deterministic crack propagation simulation method is unclear due to unclear reservoir parameters is avoided;
3. the method analyzes the influence of initial ground stress distribution, fracturing fluid injection pressure and fractal probability index on the fracture form, and has better applicability.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method of reservoir fracture network propagation path calculation in accordance with the present invention;
fig. 2 is a conceptual model of fracturing a horizontal well.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
Please refer to fig. 1, which is a flowchart illustrating a method for calculating an extended path of a fracture network of a reservoir fracture according to the present invention, comprising the following steps:
and S1, dividing the stratum into a plurality of geological unit bodies with certain sizes.
In the embodiment, a conceptual model of one three-section single-cluster fractured horizontal well is established, and half volume of a single fracture of the conceptual model is divided, as shown in fig. 2, the area of the model is 100m × 100m, geological unit bodies are divided on the basis of the model, 200 × 200 geological unit bodies are obtained through further division, the initial maximum principal stress of a stratum is 35MPa, the maximum minimum horizontal principal stress difference gradient is 0.1MPa/m, namely the maximum minimum horizontal principal stress difference from a shaft to a far part of the stratum is gradually increased, and the pore pressure of the stratum is 18 MPa.
And S2, determining an initial fracture coordinate point.
And S3, aiming at each geological unit body, when the fracturing fluid permeates into the cracks, introducing a fluid pressure drop equation to correct the flow pressure in the cracks, and calculating the pressure of the fracturing fluid permeating fluid in the cracks of the corresponding geological unit body.
Specifically, the fluid pressure drop equation is as follows:
Figure BDA0003286432110000051
wherein v isxRepresenting the fluid flow velocity up the fracture axis, μ the fluid viscosity, p the fluid pressure within the fracture, x the fracture axis direction, y the fracture width direction, and z the fracture height direction.
In one embodiment, if the fluid velocity at which the fracture is avoided is considered to be 0, the above equation will further translate to:
Figure BDA0003286432110000052
wherein w is the width of the crack;
Figure BDA0003286432110000053
a pressure gradient circumferential to the fracture; qxThe axial flow of the fracture.
S4, acquiring all reservoir geological parameters needed in the process of fracturing fracture expansion, and determining the circumferential stress distribution formed by the fracture tip and the critical fracture stress of all geological unit bodies around according to the reservoir geological parameters and the natural fracture distribution rule; the geological parameters of the reservoir comprise a ground stress field, fracture initiation critical stress, flow pressure in the fracture and stress shadow effect of the fracture.
When the horizontal well is fractured, the existing fractures change the stress distribution state of surrounding rocks and influence the expansion form of subsequent fractures, namely the stress shadow effect. Since newly created fractures may change the surrounding stress distribution, the stress field of the formation needs to be recalculated in case of a change of the surrounding stress distribution. However, since the stress shadow effect only affects the rock stress distribution near the fracture, the workload of iterative computation required due to stress redirection is reduced to a great extent by correcting the rock stress state around the newly generated fracture channel in the current embodiment, and the computation efficiency is further improved.
And S5, outputting the fracture form when the circumferential stress around the fracture tip is larger than the critical fracture stress for the geological unit body with the formed secondary fracture, and otherwise, executing the next step.
S6, calculating the fracture initiation stress intensity according to the circumferential stress and the fracture initiation critical stress; and introducing a fractal probability index, and determining the crack propagation probability of each geological unit body around the secondary crack tip according to the crack initiation stress intensity and the fractal probability index.
Specifically, in the current step, the calculating the fracture initiation stress strength according to the circumferential stress and the fracture initiation critical stress includes:
and (3) calculating the fracture initiation stress intensity according to the following formula:
Figure BDA0003286432110000061
wherein σfrStress intensity for crack initiation, σθIs the circumferential stress, σcrCritical stress for crack initiation; r is the distance from the initiation point to the tip of the fracture; theta is a stress angle; k1Is the first crack stress intensity factor, K2Is a second fracture stress intensity factor; kICFracture toughness at the tip of the fracture.
In a specific embodiment, the ground stress and the inside of the slotCombined effect of fluid pressure, first fracture stress intensity factor K1Specifically, it can be expressed as:
Figure BDA0003286432110000062
wherein alpha is an included angle between the normal direction of the crack surface and a coordinate axis; a represents the half-length of the crack; p is a radical ofnetIs the fracture net pressure.
In one specific embodiment, the second fracture stress intensity factor K is a combination of the ground stress and the fluid pressure in the fracture2The concrete expression is as follows:
Figure BDA0003286432110000071
wherein σxxAnd σyyExpressed as stress in the principal and normal directions of the fracture, respectively; alpha is an included angle between the normal direction of the crack surface and the coordinate axis; a represents the half length of the crack.
It should be noted that the fracture formed by hydraulic fracturing is an open fracture caused by a first fracture stress intensity factor, and fracture propagation is a process of brittle fracture of rock mass at the tip of the fracture, and the critical stress when the fracture is initiated is as follows:
Figure BDA0003286432110000072
s7, determining the crack propagation direction by combining the crack propagation probabilities;
specifically, in the foregoing step, the crack propagation probability is calculated by the following formula:
Figure BDA0003286432110000073
wherein σθIs the circumferential stress, σcrIs fracture initiation critical stress, eta is fractal probability index, and p (i, j) is fracture propagationProbability, N is the total number of breakdown points (sigma)θ-σcr)(i,j)The fracture initiation stress intensity at the point (i, j).
In one embodiment, the fracture simulation method based on the breakdown path assumes probability distribution P (E) that the fracture propagation rule conforms to, the higher the propagation probability of the fracture at the position with high fracture initiation stress intensity is, and the lower the propagation probability of the fracture at the position with low fracture initiation stress intensity is. Meanwhile, the randomness of crack propagation is further constrained by introducing a fractal probability index eta in the probability function of development.
And S8, correcting the stress change influence on the corresponding geological unit bodies after the fracture network extends along the fracture extension direction by adopting the stress shadow effect, and returning to the step S4 until the fracture extension does not occur any more.
Specifically, the determining the crack propagation direction by combining the crack propagation probabilities includes:
a stress difference gradient is determined, and when the stress difference gradient is larger, the crack will propagate toward the direction of the larger stress difference. When the stress difference is 0, the primary stress region at the formation level is the same in nature, and therefore, the propagation probabilities in the respective directions at the time of fracture propagation are substantially the same, and a fracture network system is more easily formed. When stress difference exists, the larger the gradient of the stress difference is, the larger the horizontal main stress is, and the smaller the energy required for crack propagation is, so that the crack is more easily propagated to a place with large stress difference, and meanwhile, branch cracks generated by the crack are relatively reduced along with the increase of the gradient of the stress difference.
And determining the injection pressure of the fracturing fluid, wherein the propagation distance of the fracture is larger when the injection pressure of the fracturing fluid is larger. It should be noted that, the reason why the extended distance becomes large currently is: when the injection pressure is increased, the energy of the fracture is further kept sufficient in the extension process, and the fracture is more prone to form more branch fractures due to the large initial pressure, and the development of the fracture network is more obvious.
Determining a fractal probability index, wherein when the fractal probability index is larger, the crack is expanded towards a breakable point. It should be noted that the crack propagation has a certain randomness, and the probability of the fracture of each possible geological unit body at each time step is directly related to the fractal probability index, so that the fractal probability index affects the selection of the crack propagation direction at each time step, thereby affecting the final shape of the whole crack. The fractal probability index only affects the local structure of the fracture, while the approximate morphology of the fracture itself will remain unchanged. And matching the micro seismic data to obtain a proper fractal probability index of the stratum.
According to the oil reservoir fracturing fracture network expansion path calculation method, the fracture expansion direction is determined by the fracturing fracture simulation method based on the breakdown path, so that the fracture expansion simulation efficiency is greatly improved; the uncertainty of the crack propagation direction is represented through the fractal probability index, so that the problem that the description of a deterministic crack propagation simulation method is unclear due to unclear reservoir parameters is avoided; the influence of initial ground stress distribution, fracturing fluid injection pressure and fractal probability index on fracture morphology is analyzed, and the method has good applicability.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (8)

1. A method for calculating an expansion path of a fracture network of a reservoir is characterized by comprising the following steps:
s1, dividing the stratum into a plurality of geological unit bodies with certain sizes;
s2, determining an initial fracture coordinate point;
s3, aiming at each geological unit body, when fracturing fluid permeates into cracks, introducing a fluid pressure drop equation to correct flow pressure in the cracks, and calculating the pressure of the fracturing fluid permeating fluid in the cracks of the corresponding geological unit body;
s4, acquiring all reservoir geological parameters needed in the process of fracturing fracture expansion, and determining the circumferential stress distribution formed by the fracture tip and the critical fracture stress of all geological unit bodies around according to the reservoir geological parameters and the natural fracture distribution rule; the geological parameters of the reservoir comprise a ground stress field, fracture initiation critical stress, flow pressure in the fracture and a stress shadow effect of the fracture;
s5, aiming at the geological unit body with the formed secondary fractures, when the circumferential stress around the fracture tips is larger than the critical fracture stress, the fracture morphology is output, and if not, the next step is executed;
s6, calculating the fracture initiation stress intensity according to the circumferential stress and the fracture initiation critical stress; introducing a fractal probability index, and determining the crack propagation probability of each geological unit body around the secondary crack tip according to the crack initiation stress intensity and the fractal probability index;
s7, determining the crack propagation direction by combining the crack propagation probabilities;
and S8, correcting the stress change influence on the corresponding geological unit bodies after the fracture network extends along the fracture extension direction by adopting the stress shadow effect, and returning to the step S4 until the fracture extension does not occur any more.
2. The method of claim 1, wherein the total number of 200 x 200 geocells obtained by dividing in step S1, and the control area of each geocell is 1m x 2 m.
3. The method according to claim 1, wherein in step S3, the fluid pressure drop equation is embodied as:
Figure FDA0003286432100000021
wherein v isxFor fluid in the fractureThe axial upward flow velocity, μ is the fluid viscosity, p is the fluid pressure within the slot,
Figure FDA0003286432100000022
is the pressure drop gradient in the axial direction of the crack,
Figure FDA0003286432100000023
is the pressure drop gradient in the width direction of the crack,
Figure FDA0003286432100000024
the pressure drop gradient in the direction of the fracture height.
4. The method according to claim 1, wherein the calculating of fracture initiation stress intensity according to the circumferential stress and the fracture initiation critical stress in step S6 comprises:
and (3) calculating the fracture initiation stress intensity according to the following formula:
Figure FDA0003286432100000025
wherein σfrStress intensity for crack initiation, σθIs the circumferential stress, σcrCritical stress for crack initiation; r is the distance from the initiation point to the tip of the fracture; theta is a stress angle; k1Is the first crack stress intensity factor, K2Is a second fracture stress intensity factor; kICFracture toughness at the tip of the fracture.
5. The method of claim 4, wherein the first fracture stress intensity factor K1The comprehensive action of the ground stress and the fluid pressure in the seam is specifically represented as:
Figure FDA0003286432100000026
wherein alpha is an included angle between the normal direction of the crack surface and a coordinate axis; a represents the half-length of the crack; p is a radical ofnetIs the fracture net pressure.
6. The method of claim 4, wherein the second fracture stress intensity factor K2The comprehensive action of the ground stress and the fluid pressure in the seam is specifically represented as:
Figure FDA0003286432100000027
wherein σxxAnd σyyExpressed as stress in the principal and normal directions of the fracture, respectively; alpha is an included angle between the normal direction of the crack surface and the coordinate axis; and a represents the half-length of the crack.
7. The method of claim 1, wherein in step S6, the determining fracture propagation probabilities for each of the plurality of geological units around the secondary fracture tip according to the fracture initiation stress intensity and a fractal probability index comprises:
the calculation of the fracture propagation probability is performed by the following formula:
Figure FDA0003286432100000031
wherein σθIs the circumferential stress, σcrIs fracture initiation critical stress, eta is fractal probability index, p (i, j) is fracture propagation probability, N is total breakdown point number, (sigma)θ-σcr)(i,j)The fracture initiation stress intensity at the point (i, j).
8. The method of claim 1, wherein the determining the crack propagation direction in combination with the crack propagation probabilities in step S7 comprises:
determining a stress difference gradient, wherein when the stress difference gradient is larger, the crack is expanded towards the direction of large stress difference;
determining the injection pressure of the fracturing fluid, wherein the larger the injection pressure of the fracturing fluid is, the larger the expansion distance of the fracture is;
determining a fractal probability index, wherein when the fractal probability index is larger, the crack is expanded towards a breakable point.
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